I'm having this same problem:
iTunes is up to date, Apple TV is up to date, routers have been reset (but there was nothing wrong with streaming anything else through Apple TV or through my PC or iPhone anyway), Windows is up to date and clear of viruses and malware. All my iTunes media is stored locally on a computer and backed up on an external disk, so the only streaming involved was from PC to TV. No iCloud or iTunes store was used. I have a 5Gbps dual band wireless router that my internal devices run on. Not a problem on the wireless side. The PC is not set to go to sleep at all, and the screen was up and showing iTunes through this entire process, so it wasn't a computer setting shutting off sharing or the application. Signal strength on all appliances was greater than 90%.
When I tried to watch a TV episode last night, I started watching it and it got about 3 minutes in and suddenly I got the error to turn on home sharing. I went out to the main menu on Apple TV and when I went back to Computers, I got the same message. I restarted Apple TV and rebooted the computer. Once that was complete, it was back and I selected the episode again.
I chose Resume, but the resume point was at least 30 seconds before I actually stopped watching. I then paused it to see if it was still loading the episode from my PC, it had loaded about half of the 42 minute episode, according to the bar. As soon as I hit play, it came back with the same error to turn on home sharing. This time I just restarted iTunes.
That did the trick and I chose resume again. This time it took me back to nearly the beginning. When I checked to see how much of it had downloaded, it was about 85% through, so I tried to fast forward. That caused the error again. This time I tried turning off sharing and turning it back on, but that didn't work. Restarting iTunes itself worked.
I resumed again and it resumed at just before the 3 minute mark. This time I did not fast forward. I got in another 12 minutes and suddenly the error was back. I restarted iTunes, hit resume on the episode, it took me back to just before the 3 minute mark again, not the 15 where I stopped watching.
By this time, it looked as if the entire episode had downloaded to the TV, so I thought that I should be good now. Not so. After watching it to nearly 20 minutes in, it did it again.
Again I restarted iTunes, and again tried resume. It took me back to the 12 minute mark, not the 20 where I was. I didn't fast forward again (fearing that would cause the error) and continued watching it over again. I got about 22 minutes into it and again I got the error that I needed to turn on sharing. Again, I restarted iTunes, and when the resume took me back to the 3 minute mark, I just turned iTunes off out of frustration, and went to the Netflix app on the Apple TV, which had no issues at all, and later YouTube, which also had no issues. I have not tried it since.
This is the first time I've had this problem and it's the same PC, same TV, same Apple TV, same HDMI cable to the TV. I've been using it for a couple years without an issue like this.
It's extremely frustrating. I hope someone has an answer to this.